Not a reader but I think DEI is out (at many places) but not building a diverse class. Even the Supreme Court noted that…so I’m not sure the essay should change from telling “your” story and what you want the college to know about you. Not sure why that should change.
Showing how you as an individual might contribute to a thriving college community will presumably not become less valuable.
And personally, I suspect that to the extent things like your ethnicity, religion, or so on are relevant to your individual story, that will remain viable material for a good essay in appropriate cases.
I note the US Supreme Court made it very clear that sort of individualized consideration is not illegal. What they think is illegal is treating people differently based just on the categorization.
So while universities may be cautious about putting formalized wrappers on relevant policies (such as named initiatives, offices, and so on), that doesn’t necessarily mean they will stop doing what the Supreme Court said they could do, namely consider your individual story.
And if that is right, if anything it will make good essays on this sort of topic, again where appropriate, all the more useful.
We had a couple of admissions presentations etc say something along the lines of “we don’t call it DEI anymore but we still have it”. I’m sure that’s pretty widespread, at least at places that believe in the principles - same thing even at my work, for example.
To me, the purpose of the essays is to give the readers an indication of who you are as a person, what makes you tick, and to sell yourself as the kind of individual that they would love to have as part of their university. If your race/ethnicity/religion/orientation/upbringing/etc. is a big part of who you are, it is fine to include it in your essays.